Modular interpolating functions for N N = 4 SYM

We construct interpolating functions fully compatible with S-duality. We then consider the problem of resumming perturbative expansions for anomalous dimensions of low-twist low-spin non-protected operators in N = 4 super Yang-Mills theory. When the rank of the gauge group is small, the interpolations suggest that anomalous dimensions of leading twist operators take their maximum value at the point τ = exp(iπ/3). For fixed spin and large enough rank, there is a level-crossing region, where the anomalous dimension of the leading twist operator reaches its maximum and then bounces back.